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BOOKTITLE = "Proceedings of the IEEE/WIC/ACM Conference on Intelligent Agent Technology (IAT'06)",
MONTH = "December",
PDF = "http://damas.ift.ulaval.ca/publications/nguyenduc_IAT06.pdf",
LOCATION = "Hong Kong, China"
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} 

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keywords = "equilibrium computation",
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  title = 	 {Brown's Original Fictitious Play},
  journal = 	 {Journal of Economic Theory},
  year = 	 {2007},
  OPTkey = 	 {},
  volume = 	 {135},
  number = 	 {1},
  pages = 	 {572-578},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{fudenberg_levine_95,
  author =       {D. Fubenberg and D. K. Levine},
  title =        {Consistency and cautious fictitious play},
  journal =      {Journal of Economic Dynamics and Control},
  year =         {1995},
  volume =       {19},
  OPTnumber =    {},
  pages =        {1065-1089},
}

@InCollection{von_Neumann_brown_50,
  author =       {J. von Neumann and G. W. Brown},
  title =        {Solutions of games by differential equations},
  booktitle =    {Contributions to the Theory of Games},
  OPTcrossref =  {},
  OPTkey =       {},
  pages =        {73-79},
  publisher = {Princeton University Press},
  year =         {1950},
}

@InCollection{khan_sun_2002,
  author = 	 {M. A. Khan and Y. Sun},
  title = 	 {Non-cooperative games with many players},
  booktitle = 	 {Handbook of Game Theory},
  OPTcrossref =  {},
  OPTkey = 	 {},
  OPTpages = 	 {},
  publisher = {North-Holland},
  year = 	 {2002},
  editor = 	 {R. J. Aumann and S. Hart},
  volume = 	 {3},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTtype = 	 {},
  chapter = 	 {46},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{radner_rosenthal_82,
  author = 	 {R. Radner and R. W. Rosenthal},
  title = 	 {Private information and pure-strategy equilibria},
  journal = 	 {Mathematics of Operations Research},
  year = 	 {1982},
  OPTkey = 	 {},
  volume = 	 {7},
  number = 	 {3},
  pages = 	 {401-409},
  month = 	 {August},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{mas-colell_84,
  author =       {A. Mas-Colell},
  title =        {On a theorem of {Schmeidler}},
  journal =      {Journal of Mathematical Economics},
  year =         {1984},
  OPTkey =       {},
  volume =       {13},
  OPTnumber =    {},
  pages =        {201-206},
  OPTmonth =     {},
  OPTnote =      {},
  OPTannote =    {}
}

@Article{schmeidler_73,
  author =       {D. Schmeidler},
  title =        {Equilibrium Points of Nonatomic Games},
  journal =      {J. of Statistical Physics},
  year =         {1973},
  OPTkey =       {},
  volume =       {7},
  number =       {4},
  pages =        {295-300},
  OPTmonth =     {},
  OPTnote =      {},
  OPTannote =    {}
}

@inproceedings{ganzfried2009computing,
  title={Computing equilibria in multiplayer stochastic games of imperfect information},
  author={S. Ganzfried and T. Sandholm},
  booktitle={Proceedings of the 21st International Joint Conference on Artificial Intelligence},
  pages = {140-146},
  year={2009}
}

@article{krishna1996simultaneous,
  title={{Simultaneous auctions with synergies}},
  author={Krishna, V. and Rosenthal, R. W.},
  journal={Games and Economic Behavior},
  volume={17},
  pages={1--31},
  year={1996},
  publisher={ACADEMIC PRESS, INC.}
}

@article{rothkopf1977bidding,
  title={{Bidding in simultaneous auctions with a constraint on exposure}},
  author={Rothkopf, M. H.},
  journal={Operations Research},
  volume={25},
  number={4},
  pages={620--629},
  year={1977},
  publisher={JSTOR}
}


@article{szentes2003three,
  title={{Three-object two-bidder simultaneous auctions: {C}hopsticks and tetrahedra}},
  author={Szentes, B. and Rosenthal, R. W.},
  journal={Games and Economic Behavior},
  volume={44},
  number={1},
  pages={114--133},
  year={2003},
  publisher={Elsevier}
}

@article{fatima2007comparison,
  title={{A comparison of sequential and simultaneous auctions}},
  author={Fatima, S. S.},
  journal={Agent-Mediated Electronic Commerce. Automated Negotiation and Strategy Design for Electronic Markets},
  pages={164--177},
  year={2007},
  publisher={Springer}
}

@article{fatima2008bidding,
  title={{Bidding strategies for multi-object auctions}},
  author={Fatima, S. S.},
  journal={Negotiation, Auctions, and Market Engineering},
  pages={200--212},
  year={2008},
  publisher={Springer}
}

@article{GerdingJAIR2008,
          volume = {32},
           month = {August},
           title = {Optimal Strategies for Bidding Agents Participating in Simultaneous Vickrey Auctions with Perfect Substitutes},
          author = {E. H. Gerding and R. Dash and A. Byde and N. R. Jennings},
            year = {2008},
           pages = {939--982},
         journal = {Journal of Artificial Intelligence Research}
}

@inproceedings{ecs13267,
       booktitle = {Sixth International Joint Conference on Autonomous Agents and Multiagent Systems},
           title = {Bidding optimally in concurrent second-price auctions of perfectly substitutable goods},
          author = {E. H. Gerding and R. K. Dash and D. C. K. Yuen and N. R. Jennings},
            year = {2007},
           pages = {267--274},
        keywords = {simultaneous auctions, optimal bidding strategies, Vickrey, second-price}
}

@inproceedings{ecs20991,
       booktitle = {19th European Conference on Artificial Intelligence (ECAI)},
           title = {An Equilibrium Analysis of Competing Double Auction Marketplaces using Fictitious Play},
          author = {B. Shi and E. Gerding and P. Vytelingum and N. R. Jennings},
            year = {2010},
           pages = {575--580}
}


@inproceedings{ecs17271,
       booktitle = {Proceedings of the 21st International Joint Conference on Artificial Intelligence},
           month = {July},
           title = {Generalised Fictitious Play for a Continuum of Anonymous Players},
          author = {Z. Rabinovich and E. H. Gerding and M. Polukarov and N.R. Jennings},
            year = {2009},
           pages = {245--250}
}

@inproceedings{ecs12600,
       booktitle = {17th European Conference on AI},
           title = {Heuristic bidding strategies for multiple heterogeneous auctions},
          author = {D. Yuen and A. Byde and N. R. Jennings},
            year = {2006},
           pages = {300--304},
         journal = {Proc. 17th European Conference on AI, Trento, Italy},
        abstract = {This paper investigates utility maximising bidding heuristics for agents that participate in multiple heterogeneous auctions, in which the auction format and the starting and closing times can be different. Our strategy allows an agent to procure one or more items and to participate in any number of auctions. For this case, forming an optimal bidding strategy by global utility maximisation is computationally intractable, and so we develop two-stage heuristics that first provide reasonable bidding thresholds with simple
strategies before deciding which auctions to participate in. The proposed approach leads to an average gain of at least 24\% in agent utility over commonly used benchmarks.}
}

@inproceedings{GerdingAAMAS08,
       booktitle = {The 7th International Conference on Autonomous Agents and Multiagent Systems},
           month = {May},
           title = {Approximating Mixed Nash Equilibria using Smooth Fictitious Play in Simultaneous Auctions},
          author = {E. H. Gerding and Z. Rabinovich and A. Byde and E. Elkind and N. R. Jennings},
            year = {2008},
           pages = {1577--1580},
        abstract = {We investigate equilibrium strategies for bidding agents that participate in multiple, simultaneous second-price auctions with perfect substitutes. For this setting, previous research has shown that it is a best response for a bidder to participate in as many such auctions as there are available, provided that other bidders only participate in a single auction. In contrast, in this paper we consider equilibrium behaviour where all bidders participate in multiple auctions. For this new setting we consider mixed-strategy Nash equilibria where bidders can bid high in one auction and low in all others. By discretising the bid space, we are able to use smooth fictitious play to compute approximate solutions. Specifically, we find that the results do indeed converge to \${$\backslash$}epsilon\$-Nash mixed equilibria and, therefore, we are able to locate equilibrium strategies in such complex games where no known solutions previously existed.}
}


@inproceedings{naroditskiy2007aaai,
  title={Using iterated best-response to find {B}ayes-{N}ash equilibria in auctions},
  author={Naroditskiy, V. and Greenwald, A.},
  booktitle={Proceedings of the 22nd Conference on Artificial Intelligence (AAAI)},
  pages={1894--1895},
  year={2007}
}

@inproceedings{reeves2004cbr,
  title={Computing Best-Response Strategies in Infinite Games of Incomplete Information},
  author={Reeves, D. M. and Wellman, M. P.},
  booktitle={Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence},
  pages={470--478},
  year={2004},
  publisher={AUAI Press Arlington, Virginia, United States}
}

@book{krishnabook,
  title={Auction theory},
  author={Krishna, V.},
  year={2009},
  edition={2nd},
  publisher={Academic press}
}

@article{engelbrecht79example, 
author = {R. Engelbrecht-Wiggans and R. Weber},
title = {An Example of a Multiobject Auction Game},
journal ={Management Science},
volume ={25},
year={1979},
pages={1272--1277}
}

@article{szentes03three,
author = {B. Szentes and R. Rosenthal},
title = {Three-Object Two-Bidder Simultaneous Auctions: {C}hopsticks and Tetrahedra},
journal={Games and Economic Behavior},
volume = {44},
year = {2003},
pages = {114--133}
}

@article{rosenthal96simultaneous, 
author={R. Rosenthal and R. Wang},
title={Simultaneous Auctions with Synergies and Common Values},
journal={Games and Economic Behavior},
volume={17},
number={1},
pages={32--55},
year={1996}
}
@article{mcafee93,
	author = {R. P. McAfee},
	title = {Mechanism Design by Competing Sellers},
	journal = {Econometrica},
	volume = {61},
	number = {6},
	pages = {1281--1312},
	year = {1993},
	ref = {eg21}
}

@article{peters97,
	author = {M. Peters and S. Severinov},
	title = {Competition among Sellers Who Offer Auctions Instead of Prices},
	journal = {Journal of Economic Theory},
	year = {1997},
	volume = {75},
	pages = {141--179},
	ref = {eg31}
}

@InProceedings{gerding07,
    author = {E. H. Gerding and A. Rogers and R. K. Dash and N. R. Jennings},
    title = {Sellers Competing for Buyers in Online Markets: {R}eserve Prices, Shill Bids, and Auction Fees},
	booktitle = {Proceedings of the 20th International Joint Conference on Artificial Intelligence},
	location = {Hyderabad, India},
	pages = {1287--1293},
	year = {2007}
}
@inproceedings{leytonbrown2000bci,
  title={Bidding Clubs: {I}nstitutionalized Collusion in Auctions},
  author={Leyton-Brown, K. and Shoham, Y. and Tennenholtz, M.},
  booktitle={Proceedings of the 2nd ACM Conference on Electronic Commerce},
  location = {Minneapolis, Minnesota, USA},
  pages={253--259},
  year={2000},
  publisher={ACM Press New York, NY, USA}
}

@article{shehory02,
	author = {O. Shehory},
	title = {Optimal Bidding in Multiple Concurrent Auctions},
	journal = {International Journal of Cooperative Information Systems},
	volume ={11},
	numbers={3--4},
	pages = {315--327},
	year = {2002}
}

@article{ecs11548,
          volume = {7},
          number = {2},
           month = {November},
          author = {E. David and A. Rogers and J. Schiff and S. Kraus and M. Rothkopf and N. R. Jennings},
           title = {Optimal Design Of English Auctions With Discrete Bid Levels},
         journal = {ACM Transactions on Internet Technology},
           pages = {Article 12},
            year = {2007},
        keywords = {discrete bids, English auction, optimal auction desig},
        abstract = {This paper considers a form of ascending price English auction widely used in both live and online auctions. This discrete bid auction requires that the bidders submit bids at predetermined discrete bid levels, and thus, there exists a minimal increment by which the bid price may be raised. In contrast, the academic literature of optimal auction design deals almost solely with continuous bid auctions. As a result, there is little practical guidance as to how an auctioneer, seeking to maximize its revenue, should determine the number and value of these discrete bid levels, and it is this omission that is addressed here. To this end, a model of a discrete bid auction from the literature is considered, and an expression for the expected revenue of this auction is derived. This expression is used to determine both numerical and analytical solutions for the optimal bid levels, and uniform and exponential bidder?s valuation distributions are compared. Finally, the limiting case where the number of discrete bid levels is large is considered. An analytical expression for the distribution of the optimal discrete bid levels is derived, and an intuitive understanding of how this distribution maximizes the revenue of the auction is developed.}
}
@article{hershberger1989finding,
  title={Finding the upper envelope of n line segments in O (n log n) time},
  author={Hershberger, J.},
  journal={Information Processing Letters},
  volume={33},
  number={4},
  pages={169--174},
  year={1989},
  publisher={Elsevier}
}

@book{abramowitz1964handbook,
  title={Handbook of mathematical functions with formulas, graphs, and mathematical tables},
  editor={Abramowitz, M. and Stegun, I.A.},
  year={1964},
  publisher={Dover publications}
}

@inproceedings{hawkin2011automated,
  title={Automated Action Abstraction of Imperfect Information Extensive-Form Games},
  author={Hawkin, J. and Holte, R. and Szafron, D.},
  booktitle={Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence},
  pages={681--687},
  year={2011}
}